SPT N-Value to Relative Density Calculator
Classify a granular soil from its Standard Penetration Test (SPT) N-value: get the Terzaghi–Peck density class, an estimated relative density Dr and an estimated friction angle φ. Geotechnical engineers and drillers use it to turn raw blow counts into first-pass strength parameters for sands.
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Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the SPT N-value (blows to drive the split-spoon the last 300 mm).
- Optionally enter the effective overburden stress σv′ (kPa) at that depth to apply the overburden correction and normalise to (N₁)₆₀.
- Read the density class, relative density Dr% and friction angle φ.
How it works
The field N is placed on the Terzaghi–Peck scale (Very loose 0–4, Loose 4–10, Medium dense 10–30, Dense 30–50, Very dense >50). If you supply the effective overburden stress, the Liao & Whitman (1986) correction CN = √(100/σv′) (capped at 1.7) scales the blow count to a reference stress of 100 kPa, giving the normalised (N₁)₆₀ ≈ CN·N — the field N is assumed to already approximate N₆₀ (60 % hammer energy).
Relative density follows Skempton (1986): Dr ≈ √((N₁)₆₀ / 60) × 100 %, capped at 100 %. The friction angle uses the Peck, Hanson & Thornburn correlation φ ≈ 27.1 + 0.3·N − 0.00054·N² (degrees). These are empirical correlations calibrated for clean sands.
Worked example
N = 20 at σv′ = 100 kPa. CN = √(100/100) = 1.00, so (N₁)₆₀ = 1.00 × 20 = 20. Dr = √(20/60) × 100 = 57.7 % (medium-dense). φ = 27.1 + 0.3×20 − 0.00054×20² = 32.9°. Terzaghi–Peck class for N = 20 is Medium dense.
Common mistakes
- Applying SPT correlations to gravels or clays — the N-value is unreliable there; these formulas are for clean sands.
- Double-correcting for energy: the field N is assumed already ≈ N₆₀, so don't re-apply a hammer-energy factor before entering it.
- Entering total (not effective) overburden stress — use σv′ (subtract pore-water pressure below the water table).
Frequently asked questions
What is a good SPT N-value for sand?
Loosely: 0–4 very loose, 4–10 loose, 10–30 medium dense, 30–50 dense, and above 50 very dense (Terzaghi–Peck). Higher N generally means higher bearing capacity and lower settlement.
What is (N₁)₆₀?
The SPT blow count corrected for both hammer energy (to 60 %) and overburden stress (normalised to 100 kPa via CN). This tool assumes your field N is already N₆₀ and applies the CN overburden correction when you enter σv′.
Why is the overburden factor CN capped?
At shallow depths √(100/σv′) grows large and would over-inflate the corrected N. Liao & Whitman's form is commonly capped at about 1.7 (some references use 2.0) to keep it realistic.
How accurate is the friction angle estimate?
The Peck correlation gives a reasonable first-pass φ for clean sands, typically ±2–3°. For design, confirm with laboratory triaxial or direct-shear testing.
Do I need the overburden stress?
No — leave it blank to get the density class, Dr and φ straight from the field N. Adding σv′ refines the relative density via the (N₁)₆₀ correction.
Related tools
- Shear Box Test Strength Parameters Calculator
- Bearing Capacity (Terzaghi) Calculator
- Void Ratio Calculator
- Soil Specific Gravity Calculator
- CPT Friction Ratio Soil Classification Tool
- Triaxial Test Mohr Circle Calculator
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Cite this tool
Zerdly. (2026). SPT N-Value to Relative Density Calculator. Retrieved from https://www.zerdly.com/tools/spt-n-value-to-relative-density-calculator/
Tip: Enter any known values to calculate the remaining results.
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